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A332512
Numbers k such that phi(k) == 0 (mod 12), where phi is the Euler totient function (A000010).
7
13, 21, 26, 28, 35, 36, 37, 39, 42, 45, 52, 56, 57, 61, 63, 65, 70, 72, 73, 74, 76, 77, 78, 84, 90, 91, 93, 95, 97, 99, 104, 105, 108, 109, 111, 112, 114, 117, 119, 122, 124, 126, 129, 130, 133, 135, 140, 143, 144, 146, 147, 148, 152, 153, 154, 155, 156, 157, 161
OFFSET
1,1
COMMENTS
Dence and Pomerance showed that the asymptotic number of the terms below x is ~ x.
LINKS
Thomas Dence and Carl Pomerance, Euler's function in residue classes, in: K. Alladi, P. D. T. A. Elliott, A. Granville and G. Tenenbaum (eds.), Analytic and Elementary Number Theory, Developments in Mathematics, Vol. 1, Springer, Boston, MA, 1998, pp. 7-20, alternative link.
EXAMPLE
13 is a term since phi(13) = 12 == 0 (mod 12).
MATHEMATICA
Select[Range[200], Divisible[EulerPhi[#], 12] &]
PROG
(Magma) [k:k in [1..170]| EulerPhi(k) mod 12 eq 0]; // Marius A. Burtea, Feb 14 2020
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 14 2020
STATUS
approved